An analytical method has been developed for determining the moment of destruction of thin pipe coatings whose material retains elasticity during cyclic changes in internal pressure. The coating material has the property of strain softening, that is, destruction with increasing deformation occurs as stresses drop. The properties of the coating material are described by a convex-concave potential. Due to damage accumulation resulting from fatigue loading, the properties of the coating material change. Hence, the complete deformation curve degenerates. To determine the moment of destruction, the methods of the mathematical theory of catastrophes are used, which make it possible to find all the equilibrium positions of the system and the point of instability of the deformation process. Due to the degeneration of the properties of the coating material, the catastrophe (loss of stability) approaches the parameters of fatigue loading.
A problem on the fracture of a thin-walled spherical vessel affected by increasing internal pressure is formulated. The material properties both in the stage of hardening and in the stage of softening (prefracture) are described. The mathematics of the catastrophe theory is used to write down the equilibrium equations and to find the critical value of pressure, at which the vessel fails.
An analytical method is developed to determine the moment of destruction of thin coatings on pipes and spherical vessels. The coating material works at the stage of elasticity; it has the property of strain softening, that is, destruction with increasing deformation occurs in the process of stress drop. The properties of the coating material are described by convex-concave potentials both under uniaxial tension and in a plane stress state. To determine the moment of destruction, methods of the mathematical theory of catastrophes are applied, which allow one to find all the equilibrium positions of systems and the point of loss of stability of the deformation process.
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